Simplify the following expression: $ q = \dfrac{4}{t + 5} - \dfrac{-8}{3} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{4}{t + 5} \times \dfrac{3}{3} = \dfrac{12}{3t + 15} $ Multiply the second expression by $\dfrac{t + 5}{t + 5}$ $ \dfrac{-8}{3} \times \dfrac{t + 5}{t + 5} = \dfrac{-8t - 40}{3t + 15} $ Therefore $ q = \dfrac{12}{3t + 15} - \dfrac{-8t - 40}{3t + 15} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{12 - (-8t - 40) }{3t + 15} $ Distribute the negative sign: $q = \dfrac{12 + 8t + 40}{3t + 15}$ $q = \dfrac{8t + 52}{3t + 15}$